2020 Fiscal Year Final Research Report
Research on algebraic cycles using cohomology and modulus
| Project/Area Number |
16K05072
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Chuo University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Keywords | 算術的スキーム / 代数的サイクル / 代数的K群 / サイクル類 / Chern類 / エタールコホモロジー / Galoisコホモロジー / 局所・大域原理 |
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| Outline of Final Research Achievements |
Through the period of this research from 2016, I have been explored how to simplify the theory of higher algebraic cycles (cycles on products of a scheme and affine spaces, as we use to defined higher Chow groups) and studied cycle classes (and higher characteristic classes) in cohomology groups. In particular, it is a nice achievement to have solved a conjecture raised by Uwe Jannsen in 1989 under some restriction on weights of \'etale cohomology in coefficients (but without any restrictions on motives), concerning a local-principal of Galois cohomology of `S-ramified' Galois groups.
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| Free Research Field |
数論幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
算術的曲面（整数係数の代数方程式系で定義されたよい図形で２次元の広がりをもつもの）のゼータ関数の s=2 での留数を有限個の素数べき倍による曖昧さを除いて記述できるような例が（何の予想も仮定せずに）構成できるようになった。
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